After all, it is possible to predict in hindsight that CERN would be perfect to develop a useful hypertext sytsem. But if one wants to use the unexpected, unpredictable benefits of a project as one of the arguments for funding, there has to be a rationale why this particular project or field is especially likely to lead to unexpected benefits.
So, big science drives technological developments in established fields, as well as occasionally resulting in new technology. [I distinguish two basic modes of technological progress: secular improvements in technology and new technologies - only the latter qualifies as "innovation" IMHO, and that is not predictable in the way that one can use, say, Moore's law when designing the specs of a computer system to be deployes 5 years in the future.] We have met the enemy, and he is us — Pogo
I would argue it's innovation all the way through. Some improvements change a subfield, and from the outside it looks as gradual, expected improvement. Some change a field, and the outside world can notice it and say it's something fundamentally different.
The difference between the dynamical systems we are used to considering in physics and biological or economic evolution is the possibility of the system of differential/difference equations changing dimensionality in response to processes within the system itself. We have met the enemy, and he is us — Pogo
But in reality, new products/inventions, even improvements on existing ones, are usually not that simple. They add an extra dimension, more freedom to find better solutions to problems. But in a high-level, low dimensional description, this freedom can be collapsed into a change in parameters, or really added as extra dimension, if the effects are important enough.
Funny thing is, I am currently working on shape optimization, where it is completely natural to change the number of parameters used to describe the shape, and thus the dimension of the problem.
A related field is order reduction, where you try to (locally) approximate a physical phenomenon by its most important modes. If there is a change in the physics, you can either modify the modes, but keep the same number of them, or you might find that for the new situation more modes are required to describe it well enough.
I would suggest this is a good analogy for your innovation/improvement distinction
I am familiar with dimension reduction (proper orthogonal modes, principal componets, factor analysis...) and you're right, at some level the number of variables is a matter of choice. But you still have to be able to close the system of equations. You can always ascribe the effect of all the neglected modes to "noise", though. We have met the enemy, and he is us — Pogo
